Lacunary Müntz systems Academic Article uri icon

abstract

  • The classical theorem of Müntz and Szász says that the span of [formula omtted] is dense in C[0,1] in the uniform norm if and only if [formula omtted]. We prove that, if [formula omtted] is lacunary, we can replace the underlying interval [0,1] by any set of positive measure. The key to the proof is the establishment of a bounded Remez-type inequality for lacunary Müntz systems. Namely if A c [0,1] and its Lebesgue measure μ(A) is at least ε>0 then [formula omtted] i = 0 A where c depends only on ε and A (not on n and A) and where [formula omtted]. © 1993, Edinburgh Mathematical Society. All rights reserved.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

citation count

  • 2

publication date

  • October 1993